The value of ∫ dx/(1 + e^x)(sin^6x + cos^6x), x ∈ -π/2, π/2 is equal to:

Question

The value of \(\int\limits^{\pi/2}_{-\pi/2} \frac{dx}{(1 + e^x)(sin^6x + cos^6x)}\) is equal to:

(1) 0

(2) 2π

(3) π

(4) π/2

Answer 1

Correct option is (3) π

Let tan x = t

⇒ sec²x dx = dt